How to draw very thin line on cube?
If you want that with geometry you could do several things.
If you don't need it to be a continuous mesh you can 
duplicate the object, and apply a Skin modifier to the new object, or a Wireframe modifier.

With the skin modifier you need to adjust the thickness in Edit Mode, on the N panel, Mean Radius, X and Y.

With the Wireframe modifier you can just adjust it globally on the modifier.

The results are visually different so you have to see what works best for you.
You can delete some of the unwanted edges on the new object too. if you don't need all the edges.

If it needs to be a continuous mesh, then you have to go by hand making all the loops and extrudes, but unless that is really necessary, I would go with the other options.

If you don't want geometry, just UVmap it and apply a texture, an image or some nodes, like Bricks or even a Colorramp.